On the Convergence of a Certain Class of Fourier Series

Jorge L. deLyra

Department of Mathematical Physics, Physics Institute, University of São Paulo

August 12, 2010 - October 15, 2011


A convergence criterion for real Fourier series, which is based solely on the behavior of the Fourier coefficients, is proposed and demonstrated in a simple case. The proof of convergence is based on a geometrical construction on the complex plane, and can be understood as an application of the Dirichlet convergence test. The class of convergent Fourier series thus defined is then extended to several other cases. The possible algorithmic applications of the result are pointed out, and the analytical character of the resulting set of limiting functions is briefly commented on.